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### A nucleus with mass number 240 breaks into ....

A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nucleus is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the binding energy in the process is:

(1) 0.9 MeV
(2) 9.4 MeV
(3) 804 MeV
(4) 216 MeV

Solution

B.E. of unfragmented nucleus = $7.6 \times 240$ MeV = $15.2 \times 120$ MeV

B.E. of fragments = $8.5 \times 120 + 8.5 \times 120$ MeV = $17 \times 120$ MeV

Gain in B.E. = $17\times 120 - 15.2 \times 120$ MeV = $1.8 \times 120$ MeV = 216 MeV

A man starts walking from the point P (-3, 4), touches the x-axis at R, and then turns to reach at the point Q (0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50 [(PR)^2 + (RQ)^2 ]$ is equal to _ _ _ _ . Solution For time to be minimum at constant speed, the directions must be symmetric. In other words, the angles made by PR and RQ with the vertical must be the same just like in the law of reflection in optics. $tan \theta = \frac {MP}{MR} = \frac {NQ}{NR}$ $\Rightarrow \frac {3-r}{4} = \frac {r}{2}$ $\Rightarrow r=1$ So, $R \equiv ( - 1,0)$ Now, $50(PR^2+RQ^2)=50[(4+16)+(1+4)]=1250$